K.UNGL. SV. VET. AKADEMIENS HANDLINGAR. BAND 60- N:0 8. 17 



If we take the mean of these determinations, vve obtain the following new 

 determination of e' 



s'<0 ; 012. 



Considering that Russell 5 s formula takes into account the considerable disper- 

 sion in M appearing in the spectral class F on account of the division, beginning 

 there, between the giant and dwarf series, and with regard to the circumstance that 



m 



at the above-mentioned calculations also negative colour-indices amounting to — 0,4 

 have been attributed to ^4-stars, we must hold the opinion that the value obtained 

 for e' is an upper limit. This conclusion is also confirmed by the circumstance that 

 Shapley's colour-indices, reduced to the Harvard North Polar sequence, vvould obtain 



m 



as great negative values as- 0,7, a circumstance showing that Shapley's colour-indices 

 are not possibly due to a systematic error in the Mount Wilson scale, on which his 

 investigations are based. 



Thus we have obtained the following determinations of &': 



e' < 0,03 (From the total motions) 



s'< 0,oi2 (From Russell's & Charlier's data for the absolute magnitudes) 



s' =0,009 (From the luminosity-curves according to (3)) 



s' = 0,005 (From the luminosity-law according to graphical construction) 



e'< 5 oi4 



In view of the fact that the first value indicates only an upper limit, and in 

 reality is certainly lower, it will be justified to round off e' downwards and suppose 

 as a definitive value: 



;' = 0,oi. 



We consequently obtain the system of hypothetic parallaxes, which is given 

 in the adjoining table. The concordance with Shapley's parallaxes is particularly 

 good, and even though future determinations will somewhat modify the results, it 

 will, nevertheless, be considered as shown that Charlier's parallax-system cannot 

 be accepted without coming into collision with our present knowledge as to tfce 

 motions of globular dusters, as to the distribution of apparent magnitudes in the 

 objects that have been previonsly examined, and with the conceptions of the abso- 

 lute magnitudes of the nearer as well as of the remoter stars. 



By using the luminosity-law I have obtained smaller parallax- values than van 

 Schouten, from whose parallax-estimations e' would obtain the value 0.03. The data 

 given by Shapley as regards the estimation of the parallax of the Hercules duster, 

 at which he has also used Kapteyn's luminosity-curves and obtained smaller parallax 

 values than mine, give a value for e' of only ; ooi3. Since van Schoutek's treatise has 

 not been accessible to me, and Shapley does not mention the form of the luminosity- 

 law, on which he has based his determinations, but gives only the final results, it 



K. Sv. Vet. Akad. Handl. Band 60. N:o 8. 3 



